The specific method to include a junior business partner depend on the role of the partner.

-working partner? Then he may join as vice-president, director, director of R&D, director of finances, director of strategic planning, director/advisory... he may take a salary as equity or cash. Simply write a contract agreement with him/her and both sign the documents, if he trusts you enough to retain the entity as Sole Prop.

-nonworking partner? He might be an investor. If he wishes to be a formal investor, then you need to incorporate your business as LLC or C-Corp. You may incorporate it as a close-c-corp that limits the number of shareholders as well as it is not a publicly traded corporation. All other corporate laws are applicable. A close-corp may also help you include more shareholders, often up to 20 or 30 depending in the state of incorporation.

-simply partner without any specific role for the junior partner? Then try "partnership" business. The ratio of stakes may be agreed upon, and the company registered as partnership organization. A CPA or a Lawyer may be able to get this done in one day for a nominal fee.